Interacting with parallel coordinates

Parallel coordinate visualizations have a reputation of being difficult to understand, expert-only representations. We argue that this reputation may be partially unfounded, because many of the parallel coordinate browser implementations lack essential features. This paper presents a survey of current interaction techniques for parallel coordinate browsers and compares them to the visualization design guidelines in the literature. In addition, we report our experiences with parallel coordinate browser prototypes, and describe an experiment where we studied the immediate usability of parallel coordinate visualizations. In the experiment, 16 database professionals performed a set of tasks both with the SQL query language and a parallel coordinate browser. The results show that although the subjects had doubts about the general usefulness of the parallel coordinate technique, they could perform the tasks more efficiently with a parallel coordinate browser than with their familiar query language interface.     

The plane with parallel coordinates

By means ofParallel Coordinates planar “graphs” of multivariate relations are obtained. Certain properties of the relationship correspond tothe geometrical properties of its graph. On the plane a point ←→ line duality with several interesting properties is induced. A new duality betweenbounded and unbounded convex sets and hstars (a generalization of hyperbolas) and between Convex Unions and Intersections is found. This motivates some efficient Convexity algorithms and other results inComputational Geometry. There is also a suprising “cusp” ←→ “inflection point” duality. The narrative ends with a preview of the corresponding results inR ^N .     

Two axes re-ordering methods in parallel coordinates plots

Visualization and interaction of multidimensional data are challenges in visual data analytics, which requires optimized solutions to integrate the display, exploration and analytical reasoning of data into one visual pipeline for human-centered data analysis and interpretation. Even though it is considered to be one of the most popular techniques for visualization and analysis of multidimensional data, parallel coordinate visualization is also suffered from the visual clutter problem as well as the computational complexity problem, same as other visualization methods in which visual clutter occurs where the volume of data needs to be visualized to be increasing. One straightforward way to address these problems is to change the ordering of axis to reach the minimal number of visual clutters. However, the optimization of the ordering of axes is actually a NP-complete problem. In this paper, two axes re-ordering methods are proposed in parallel coordinates visualization: (1) a contribution-based method and (2) a similarity-based method.The contribution-based re-ordering method is mainly based on the singular value decomposition (SVD) algorithm. It can not only provide users with the mathmetical theory for the selection of the first remarkable axis, but also help with visualizing detailed structure of the data according to the contribution of each data dimension. This approach reduces the computational complexity greatly in comparison with other re-ordering methods. A similarity-based re-ordering method is based on the combination of nonlinear correlation coefficient (NCC) and SVD algorithms. By using this approach, axes are re-ordered in line with the degree of similarities among them. It is much more rational, exact and systemic than other re-ordering methods, including those based on Pearson’s correlation coefficient (PCC). Meanwhile, the paper also proposes a measurement of contribution rate of each dimension to reveal the property hidden in the dataset. At last, the rationale and effectiveness of these approaches are demonstrated through case studies. For example, the patterns of Smurf and Neptune attacks hidden in KDD 1999 dataset are visualized in parallel coordinates using contribution-based re-ordering method; NCC re-ordering method can enlarge the mean crossing angles and reduce the amount of polylines between the neighboring axes.     

A novel virtual node approach for interactive visual analytics of big datasets in parallel coordinates

Big data is a collection of large and complex ​datasets that commonly appear in multidimensional and multivariate data formats. It has been recognized as a big challenge in modern computing/information sciences to gain (or find out) due to its massive volume and complexity (e.g. its multivariate format). Accordingly, there is an urgent need to find new and effective techniques to deal with such huge ​datasets. Parallel coordinates is a well-established geometrical system for visualizing multidimensional data that has been extensively studied for decades. There is also a variety of associated interaction techniques currently used with this geometrical system. However, none of these existing techniques can achieve the functions that are covered by the Select layer of Yi’s Seven-Layer Interaction Model. This is because it is theoretically impossible to find a select of data items via a mouse-click (or mouse-rollover) operation over a particular visual poly-line (a visual object) with no geometric region. In this paper, we present a novel technique that uses a set of virtual nodes to practically achieve the Select interaction which has hitherto proven to be such a challenging sphere in parallel coordinates visualization.     

Historical data analysis based on plots of independent and parallel coordinates and statistical control limits

Interactive multidimensional visualisation based on parallel coordinates has been studied previously as a tool for process historical data analysis. Here attention is given to improvement of the technique by the introduction of dimension reduction and upper and lower limits for separating abnormal data to the plots of coordinates. Dimension reduction using independent component analysis transforms the original variables to a smaller number of latent variables which are statistically independent to each other. This enables the visualisation technique to handle a large number of variables more effectively, particularly when the original variables have recycling and interacting correlations and dependencies. Statistical independence between the parallel coordinates also makes it possible to calculate upper and lower limits (UL and LL) for each coordinate separating abnormal data from normal. Calculation of the UL and LL limits requires each coordinate to satisfy Gaussian distribution. In this work a method called the Box–Cox transformation is proposed to transform the non-Gaussian coordinate to a Gaussian distribution before the UL and LL limits are calculated.     

A new approach to line and line segment clipping in homogeneous coordinates

The clipping operation is still the bottleneck of the graphics pipeline in spite of the latest developments in graphical hardware and a significant increase in performance. Algorithms for line and line segment clipping have been studied for a long time and many research papers have been published so far. This paper presents a new robust approach to line and line segment clipping using a rectangular window. A simple extension for the case of convex polygon clipping is presented as well. The presented approach does not require a division operation and uses homogeneous coordinates for input and output point representation. The proposed algorithms can take advantage of operations supported by vector–vector hardware. The main contribution of this paper is a new approach to intersection computations applied to line and line segment clipping. This approach leads to algorithms that are simpler, robust, and easy to implement.     

基于平行坐标的贝叶斯可视化分类方法

结合信息可视化与机器学习技术,提出一种基于多元数据平行坐标图表示的贝叶斯可视化分类方法。该方法基于类条件概率密度估计对平行坐标图表示进行优化,最后对变换后的各变量值加权求和,用贝叶斯法则分类。这种方法通过平行坐标来使不可见的数据和算法变得可见,从而易于利用专家领域知识,分类结果容易理解,特别适合应用到疾病诊断等医学领域的模式识别问题。     

A parallel processing architecture for sensor-based control of intelligent mobile robots

Parallel processing plays an important role in sensor-based control of intelligent mobile robots. This paper describes the design and implementation of a parallel processing architecture used for real-time, sensor-based control of mobile robots. This architecture takes the form of a network of sensing and control nodes, based on a novel module that we call Locally Intelligent Control Agent (LICA). It is a hybrid control architecture containing low-level feedback control loops and high-level decision making components. All the sensing, planning, and control tasks for intelligent control of a mobile robot are distributed across such a network, and operate in parallel. It has been used successfully in many experiments to perform planning and navigation tasks in real-time. Such a generic architecture can be readily applied to many diverse applications.     

基于平行坐标的多个体绘制参数的优化调节*

提出基于平行坐标概念的参数控制平台来对体绘制中多个参数进行优化调节的方法。参数控制平台提供了一种调节和控制绘制参数的简单而有效的界面,它能把所有相关参数组织在一个空间,并且给用户同时显示所有参数配置的一个视图。用户可以在参数控制平台记录不同的历史绘制参数,并在一个空间对不同的参数进行比较,用户还可以重组不同的优化参数以生成新的绘制。参数控制平台有效地提高了用户对多个绘制参数进行优化调节的效率。     

单目平行线约束下的空间点坐标恢复

提出一种从单目像机拍摄的二维投影图像中恢复空间点三维坐标的简化算法.假定摄像机与空间中的一对平行线的位置关系已知,同时摄像机坐标系下平行线所在平面中的任意空间点在像平面中的投影也已知,通过射影几何可得图像坐标到目标点三维空间坐标的转换系数,即坐标转换因数,从而估计出三维空间点的坐标.实验中通过对人体行走轨迹进行估计来测试算法性能,结果表明算法简单有效,计算开销小.     

平行坐标轴动态排列的地理空间多维数据可视分析

目的 平行坐标是经典的多维数据可视化方法,但在用于地理空间多维数据分析时,往往存在空间位置信息缺失和空间关联分析不确定等问题。对此,本文设计了一种有效关联平行坐标和地图的地理空间多维数据可视分析方法。方法 根据多维属性信息对地理空间位置进行聚类分析,引入Voronoi图和颜色明暗映射对地理空间各类区域进行显著标识,利用平行坐标呈现地理空间多维属性信息,引入互信息度量地理空间聚类与属性类别的相关性,动态地确定平行坐标轴排列顺序,进一步计算属性轴与地图之间数据线的绑定位置,对数据线的布局进行优化处理,降低地图与平行坐标系间数据线分布的紊乱程度。结果 有效集成上述可视化设计及数据分析方法,设计与实现一种基于平行坐标轴动态排列的地理空间多维数据可视化分析系统,提供便捷的用户交互模式,通过2组具有明显地理空间多维属性特征的数据进行测试,验证了本文可视分析方法的有效性和实用性。结论 本文提出的可视分析方法和工具可以帮助用户快速分析地理空间多维属性存在的空间分布特征及其关联模式,为地理空间多维数据的探索提供了有效手段。     

基于衍生多边形的混合坐标

将多边形三角化,利用三角网格将三角形衍生为点多边形、边多边形和面多边形,再根据已有的重心坐标提出基于衍生多边形的混合坐标.首先在三角网格内根据初始多边形内部一点所在的三角形得到衍生多边形,然后使用调和坐标、局部重心坐标、迭代坐标中任意一种计算衍生多边形的顶点关于初始多边形顶点的重心坐标,再使用迭代坐标计算初始多边形内部...     

An efficient parallel algorithm for finding rectangular duals of plane triangular graphs

We present an efficient parallel algorithm for constructing rectangular duals of plane triangular graphs. This problem finds applications in VLSI design and floor-planning problems. No NC algorithm for solving this problem was previously known. The algorithm takesO(log² n) time withO(n) processors on a CRCW PRAM, wheren is the number of vertices of the graph.This research was supported by NSF Grants CCR-9011214 and CCR-9205982.     

基于极坐标的树木叶片特征提取方法

提出了一种在极坐标下进行特征提取的方法,并将其应用于树木叶片图像识别中。该方法首先将目标图像二值化并映射到极坐标下,提取具有旋转、缩放、平移不变性的曲线面积比率、跨度比、饱和度和高度变化率等特征。然后通过最小欧式距离对叶片进行计算、识别。该方法克服了直角坐标系下特征提取方法计算量大,花费的时间长的缺陷。基于该方法的叶片特征提取算法的时间复杂度为[O(n)]。对于叶型有区分,且需要快速进行树叶识别的树叶数据集有很好的效果。该方法在常见的13种树木叶片中进行测试,平均正确识别率达到90%以上。     

A nature inspired intelligent water drops evolutionary algorithm for parallel processor scheduling with rejection

Scheduling has become a popular area for artificial intelligence and expert system researchers during last decade. In this paper, a new metaheuristic algorithm entitled intelligent water drops (IWD) is adapted for solving a generalized kind of order scheduling problem where rejection of received orders is allowed with a penalty cost. At the beginning of production period, a set of orders are received by manufacturer. Due to capacity limit, the manufacturer can only process a subset of orders and has to decide to reject some of undesirable orders. The accepted orders are proceed to be scheduled by a set of identical parallel processors in shop floor. The objective is to select the best set of orders with high contribution in manufacturer's benefit and then find the appropriate schedule of accepted orders minimizing the number of tardy orders. To effectively solve the suggested problem, the Lexicographic utility function is customized to address different objectives and then an IWD algorithm, which is based on the process of the natural rivers and the interactions among water drops in a river, is devised. To further enhance the performance of basic IWD, an Iterated Local Search (ILS) heuristic is also incorporated into the main algorithm. To demonstrate the applicability of suggested problem and also show the effectiveness of enhanced IWD with ILS, a real-world application in commercial printing industry is presented and the performance of algorithm is compared with traditional algorithms like GA, DE and ACO.     

Six-Dimensional space expression of workspace of six-DoF parallel manipulators using hyper spherical coordinates (HSC)

A closed-form formulation for the workspace of N-Degrees-of-Freedom (DoF) parallel mechanisms is presented using least-square curve fitting. The concepts of multi-dimensional polynomial (MDP) and in hyper spherical coordinates (HSC) are introduced. The boundary of workspaces of those parallel linkages which are surfaces without voids and concavities can be well approximated by the MDPs in the HSC. First, the boundary points are obtained in HSC considering all physical constrains and probable singularities. Then, an MDP with proper order consisting of sine and cosine functions is fitted to those points. The presented method is general and applicable to all DoF. Three case studies of 2, 3, and 6-DoF mechanisms are investigated to demonstrate the effectiveness of the method.     

Positive Gordon–Wixom coordinates

We introduce a new construction of transfinite barycentric coordinates for arbitrary closed sets in two dimensions. Our method extends weighted Gordon–Wixom interpolation to non-convex shapes and produces coordinates that are positive everywhere in the interior of the domain and that are smooth for shapes with smooth boundaries. We achieve these properties by using the distance to lines tangent to the boundary curve to define a weight function that is positive and smooth. We derive closed-form expressions for arbitrary polygons in two dimensions and compare the basis functions of our coordinates with several other types of barycentric coordinates.     

基于并行打印适配器实现的双机通信

本文介绍了并行打印适配器在两台PC机之间实现双机通信中的应用。给出了一种线路连接图，和发送接收程序，并指出了进一步的工作方向。     

Efficient parallel processing with spin-wave nanoarchitectures

In this paper, we study the algorithm design aspects of three newly developed spin-wave architectures. The architectures are capable of simultaneously transmitting multiple signals using different frequencies, and allow for concurrent read/write operations. Using such features, we show a number of parallel and fault-tolerant routing schemes and introduce a set of generic parallel processing techniques that can be used for design of fast algorithms on these spin-wave architectures. We also present a set of application examples to illustrate the operation of the proposed generic parallel techniques.